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Elements of Arches |
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Formula |
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To find the rise when radius and
span are given |
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_______
H = r - ½ √4r2 - S2 |
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To find the inside radius when
rise and span are given |
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R = S2 + 4H2
8H |
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To find the angle 0 when the
radius and span are given |
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Sin ½ Ø = S
2r |
To find the lengths when the
radius and central angle are given
Outer arc :
Inner arc : |
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A = 2π
R Ø
a = 2π
r Ø
360
360 |
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Key To Symbol |
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S |
Span
of arch |
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H |
Rise
of arch |
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R |
Outside
radius of arch |
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r |
Inside
radius of arch |
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T |
Thickness of arch |
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A |
Outer
arch length |
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a |
Inner
arch length |
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e |
Central
Angle |
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Value For Given Rises Per Foot Span |
Rise in
Inches
Per
Foot Of
Span |
Inside *
Arc is
Factor
xS |
Central Angle |
Inside *
Arc is
Factor
xS |
Diff. of
Outer and Inner Arcs Factor xT |
Skewback |
Degrees
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Part of
Circle |
X * is
Factor xT |
Y * is
Factor xT |
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1 |
1.5417 |
37" 50.9' |
0.1051 |
0.0184 |
0.0184 |
0.3243 |
0.9460 |
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1¼ |
1.2521 |
47" 4.4' |
0.1308 |
1.0287 |
1.0287 |
0.3993 |
0.9168 |
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1½ |
1.0625 |
56" 8.7' |
0.1560 |
1.0412 |
1.0412 |
0.4706 |
0.8824 |
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1.608 |
1.0000 |
60" 0.0' |
0.1667 |
1.0472 |
1.0472 |
0.5000 |
0.8660 |
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1¾ |
0.9301 |
65" 2.5' |
0.1807 |
1.0558 |
1.0558 |
0.5376 |
0.8432 |
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2 |
0.8333 |
73" 44.4' |
0.2048 |
1.0725 |
1.0725 |
0.6000 |
0.8000 |
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2¼ |
0.7604 |
82" 13.4' |
0.2284 |
1.0913 |
1.0913 |
0.6575 |
0.7534 |
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2.302 |
0.7474 |
83" 58.5' |
0.2333 |
1.0954 |
1.0954 |
0.6690 |
0.7433 |
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2½ |
0.7072 |
90" 28.8' |
0.2513 |
1.1120 |
1.1120 |
0.7101 |
0.7041 |
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2¾ |
0.6600 |
98" 29.7' |
0.2736 |
1.1346 |
1.1346 |
0.7575 |
0.6528 |
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3 |
0.6250 |
106" 15.6' |
0.2952 |
1.1591 |
1.1591 |
0.8000 |
0.6000 |
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| * Inside
radius, inside arc, difference of outer and inner arcs, x and
y arcs, x and y are obtained by multiplying the factor in
respect with S or T, whichever applies. |
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